transformations translation “slide” left: subtract from x-coordinate right: add to x-coordinate...

Transformations

Translation “Slide”• Left: subtract from x-coordinate• Right: add to x-coordinate• Down: subtract from y-coordinate• Up: add to y-coordinate

Rotation “Turn”• 90° Clockwise (x, y) (y, -x)• 180° (x,y) (-x, -y)• 90° Counterclockwise (x,y) (-y, x)

Reflection “Flip”• Over x-axis (x,y) (-x, y)• Over y-axis (x,y) (x, -y)

Dilation “Enlarge/Shrink”• Multiply each coordinate by the scale factor • >1 figure enlarges• 0<sf>1 figure shrinks

Preimage- is the original figureImage- is the new figure. Labelled with ‘tick marks’.

Slope (Rate of Change)

Types of Slope

Positive Negative

Undefined Zero

Slope formula

Y2 – Y1

X2 - X1

Slope from Table

Slope Intercept Form

Slope Intercept Form Example:

Equation from Two Points

Graphing with slope andY-intercept

• Plot the y-intercept (b) on the y-axis• Count Rise and Run from that point to makesecond point• Connect points to formline.

Volume

Cylinder Cone Sphere

Pythagorean Theorem

Relationships of Lines and Angles

Rules of Exponents

Scientific Notation

The decimal moved 6 places to left.

The decimal moved 3 places to the right.

Scatterplots and Two-Way Tables

Positive relationship or association

Negative relationship or association

No relationship or association

Totals are the same across and down

Functions

Linear vs. Nonlinear

Linear Functions:• Makes a straight line• No exponent on a variable Ex. Y= X2 + 2• No multiplication or division by a variable Ex. XY = 3

Systems of Equations

Solutions are where the lines intersect.

Giving an ordered pair that satisfies both equations.

Ex. Y = X – 2 solution is (4, 2) Y =

Irrational and Repeating

Irrational Numbers are decimals that do not repeat or terminate. Therefore, can not be written as a fraction.

Ex. ∏ Ex.

Repeating decimals can be written in the form of a fraction by placing the repeating number in numerator and a denominator of 9s for each repeating digit.

Ex. 0.4 =

Equations

Ex. 5(X + 4)= 7X – 26 5X + 20 = 7X – 26 - 20 -20 5X = 7X – 46 -7X = -7X – 46 -2X = - 46 -2 -2 X = 23

NO SOLUTION

Ex. 2X – 8X + 1 = 9 – 6X -6X + 1 = 9 – 6X +6X = +6X 1 = 9 + 0X 1 = 9

INFINITE/ ALL REAL SOLUTION

Ex. 19X + 10 – 4X = 5(3X + 2) 15X + 10 = 15X + 10 *Notice that both sides are exactly the same.

ONE SOLUTION

Estimating Square/Cube Roots

falls between

3√82 falls between 3√64

√9 √163√125

0 1 2 3 4

0 1 2 3 4 5